PsychologyDescriptive StatisticsA-Level
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Standard Deviation (Sample) Calculator

Measure of the amount of variation or dispersion in a set of values.

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Sample Standard Deviation

Formula first

Overview

The sample standard deviation is a measure of dispersion that quantifies the spread of data points around the arithmetic mean. Unlike the population version, it utilizes Bessel's correction (n - 1) to provide an unbiased estimate of the population variability from a subset of data.

Symbols

Variables

s = Sample Standard Deviation, \Sigma (x - \bar{x})^2 = Sum of Squares, n = Sample Size

Sample Standard Deviation
Sum of Squares
Sample Size

Apply it well

When To Use

When to use: Apply this formula when you have collected data from a sample and want to generalize the findings to a larger population. It is the standard choice for most psychological experiments where measuring every member of a population is impossible.

Why it matters: It allows researchers to understand the consistency of behavior or cognitive performance across participants. High standard deviations indicate significant individual differences, while low values suggest the group is relatively homogeneous.

Avoid these traps

Common Mistakes

  • Dividing by n instead of n-1 for sample data.
  • Forgetting to take the square root at the very end.

One free problem

Practice Problem

A researcher measures the stress levels of 5 subjects and determines the Sum of Squares (SS) is 40. Calculate the sample standard deviation (SD).

Sum of Squares40
Sample Size5

Solve for:

Hint: Divide the SS by (n - 1) and then take the square root of the result.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Standard deviation
  2. Aron, A., Aron, E. N., & Coups, E. J. (2013). Statistics for Psychology (6th ed.). Pearson.
  3. Gravetter, F. J., Wallnau, L. B., Forzano, L. B., & Witnauer, J. E. (2021). Statistics for the Behavioral Sciences (12th ed.).
  4. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
  5. Gravetter, F. J., Wallnau, L. B., Forzano, L. B., & Witnauer, J. E. (2021). Essentials of Statistics for the Behavioral Sciences (10th ed.).
  6. Wikipedia: Bessel's correction
  7. AQA Psychology for A Level Year 1 & AS by Cara Flanagan, Dave Berry, Matt Jarvis, and Rob Liddle (or similar A-Level Psychology textbook)